EN
indefinite inner product space Krein space Hilbert space with an indefinite metric Indefinite Hilbert space Pesonen operator
EN
In mathematics, in the field of functional analysis, an indefinite inner product space {\displaystyle } is an infinite-dimensional complex vector space K {\displaystyle K} equipped with both an indefinite inner product ⟨ ⋅, ⋅ ⟩ {\displaystyle \langle \cdot,\,\cdot \rangle \,} and a positive semi-definite inner product = d e f ⟨ x, J y ⟩, {\displaystyle \ {\stackrel {\mathrm {def} }{=}}\ \langle x,\,Jy\rangle,} where the metric operator J {\displaystyle J} is an endomorphism of K {\displaystyle K} obeying J 3 = J.
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